A new method of matrix template matching is presented in the context of pulsar timing analysis. Pulse arrival times are typically measured using only the observed total intensity light curve. The new technique exploits the additional timing information available in the polarization of the pulsar signal by modeling the transformation between two polarized light curves in the Fourier domain. For a number of millisecond pulsars, arrival time estimates derived from polarimetric data are predicted to exhibit greater precision and accuracy than those derived from the total intensity alone. Furthermore, the transformation matrix produced during template matching may be used to calibrate observations of other point sources.